Commit only to a skill test you are performing, and only if the difficulty of that test is at least 2 higher than your base skill value.
Three is fantastic. I love the restriction, it feels thematic and inline with other cards like Lucky!, Oops! and "Look what I found!". When it works it is incredibly helpful however I have found it a bit of a dead card often sacrificed to Wendy Adams ability. It's probably better including Unexpected Courage and other skill cards with more versatility rather than risk having a dead card in your deck.
This card raises a question with regards to base skill vs skill value. As other people have pointed out, this card will synergize with Dark Horse but not Duke since Duke effects your base skill, but Dark Horse simply grants you a bonus. Given that Dark Horse shores up all the skill icons (, , , and ) it is safe to assume that any other asset that grants a passive icon boost such as Peter Sylvestre or Moonstone would also apply here.
I bring these up because if I am playing Calvin Wright or Patrice Hathaway with their measly 0 or 2 in the majority of their stats, it isn't all that uncommon to find 4 value targets to pitch Rise to the Occasion, putting you at +1, then whatever additional bonuses you gain from your assets or additional committed cards. Coincidentally, running upgraded Peter, Moonstone, Dark Horse, +1 from Dig Deep, puts me at a 9 vs 5 when dealing with Watcher from Another Dimension, and all I had to do was pitch this and spend a resource. What I'm saying is, RTTO gives you one up or at least evens the odds of a particularly difficult test, and then it's up to you to do the rest of the legwork. If the test is important, then you'll be glad to have this card along.
The philosophy of the card isn't to make you succeed though; it's designed to give you a fighting chance at a skill test you ordinarily would have no business attempting. You might wonder why you'd attempt to do something you aren't good at to begin with, but I'd argue that comes up far more often than you might think, especially in solo, and especially if you have specific goals you want to achieve.
This card would be helpful for someone like "Ashcan" Pete because you can only use Duke for Fight Actions, which means you can't use him to break down Locked Doors or to break into the Museum Halls, and don't even think about making a Parley. You also might need just one more hit on enemies with 3 or 5 hit points. Most scenarios do in fact have enemies and shroud values of 4, and sometimes even 5. William Yorick and Rita Young both might like a copy for checks on Treacheries of 5 (combined with Guts, not instead of, is the key. Or like I mentioned, combined with Dark Horse, Peter, etc.) or for tests on high shroud values, especially if playing solo or if there isn't a in the group for whatever reason. Or if you're simply seperated. The rule of thumb is to be 2 up, so in most cases, you'll only need one other card to pitch, but you don't even need to do that if you've got an asset or two giving you passive +1's everywhere.
The trick with this card, I think, is to know which stat you'll intend to use it for when adding it to your deck. If you have 2 , then most likely you'll use it with that. If you have low , then hold onto it for that lethal encounter card. And who knows, you might find yourself facing those rare 6 shroud or combat values, and suddenly you have a shot against something you couldn't have predicted.
This card shines best in a Charlie Kane deck in my opinion. For him, with 1 in every stat, it's just an unexpected courage with an extra icon on it (and you can collect it with a resourceful later). The game is almost entirely composed of tests that are (3) or more difficulty.
This card work realy well with Calvin Wright because all of his base skill values are 0 :)
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This Card can be played after Double or Nothing, as it raises the difficulty (if the resulting difficulty is 2 higher than your base value). This card refers to the modified difficulty of a test, not the base value.
Of the triple skills available at the time, I think that Rise to the Occasion is one of the more difficult ones to use. If the test is that much more difficult than your base skill level, then this card alone is probably not enough to guarantee a success - chances are you're going to need a little extra help.
Generally speaking, I'd normally rather have Unexpected Courage - it's one less icon, but it's much more flexible.
The exception, of course, is Calvin Wright. With base skill values that are all 0, he can use this card on almost every test. In most instances I think he's going to want to take this one with him!
Since no-one seems to have noticed, ill just point out that this card fits perfectly into any deck using Dark Horse, where it's restriction is suddenly "at least 1 higher". For Dark Horse Duke ("Ashcan" Pete), This is basically the perfect skill card to go with all your passive stat boosters.
Of course, Even for Dark Horse its basically a 3rd and 4th copy of Unexpected Courage.